Optimization Problem

A rectangle PQRS is inscribed in the region between the x-axis and the part of the graph y= cos 4x specified by -pi/8 < x< pi/8. ( the < sign is less than or equal to). Determine the coordinates of P for which the perimeter of PQRS is a maximum.

A rectangle PQRS is inscribed in the region between the x-axis and the part of the graph y= cos 4x specified by -pi/8 < x< pi/8. ( the < sign is less than or equal to). Determine the coordinates of P for which the perimeter of PQRS is a maximum.

Im not even sure where to begin...

Did you draw a diagram?

the height of the rectangle is cos(4x), the length of the rectangle is 2x (we denote the distance from the y-axis to the right bottom corner of the rectangle to be x)

now that you know the height and length of the rectangle, can you continue?

yip... P'' is -ve hence P is concave down and its a max, so for the given domain the value for x would be pi/24..
thanks for all the help... sorri for all the problems with this one...
i need help with another one im gonna post... if you can please take a look
thanks agian

yip... P'' is -ve hence P is concave down and its a max, so for the given domain the value for x would be pi/24..
thanks for all the help... sorri for all the problems with this one...
i need help with another one im gonna post... if you can please take a look
thanks agian